A detail numerical analysis of the effect of particle diameter of a packed bed of spherical particles on forced convection about an embedded circular cylinder is presented. This parametric study focusses on the two-phase energy (LTNE local thermal non-equilibrium) model, which does not assume local thermal equilibrium (LTE) between the solid medium and the fluid. The investigation is performed for a cylinder-to-particle diameter ratio D-cy/d(p) = 10-100, at a wide ranges of Reynolds number Re-D = 1-250 and solid-to-fluid thermal conductivity ratio k(r) = 0.01-1000. A comparison of predictions from the LTNE and LTE energy models is also made. This paper quantifies the influence of the key non-dimensional parameters on the heat transfer rate. It is also shown that although the presence of the porous materials around the heated cylinder enhances the overall heat transfer and increases the pressure drop in the bed compared to an empty channel, using a porous medium with large particle diameters increases considerably this enhancement in heat transfer and decreases significantly the unfavorable pressure drop. (C) 2012 Elsevier Ltd. All rights reserved.